I suggest you try tracking down Rowan Emberson who has done lots of invertebrate work on the Chatham Islands - he was based at Lincoln University so try asking there (I think he has retired but they should be able to help). In my work on the Chatham Islands I never saw any invertebrates visiting flowers, plants seem to set plenty of seed in the wild and in cultivation so it may not have a critical need for a pollinator. However, I really don't know, and like with much of our flora what you ask about here merely highlights what we don't know and really need to study better.